Export a smoke simulation as a mesh
There's not an easy way to convert a smoke simulation into a mesh; not in Blender at least. I would suggest a different tactic.

Instead of using the smoke simulator, use the fluid simulator. They both use the same basic algorithm. You'll need to toy with the inflow, gravity, and initial force settings. The main difference is that the fluid simulator doesn't deal with turbulence and heat like the smoke simulator does; you'll need to fake it a bit. However the fluid simulator does generate a sequences of meshes as its output. Any of those meshes (stored as .bobz files on your hard drive) can be converted to a "proper mesh" that you can edit and ultimately export as an STL for printing.